In contrast the conventional SE, the goal of SNRi target training is to control SNRi of the SE output \(\mathbf {y}_{:, 1}\)  according to a target SNRi scalar \(\lambda \) . To achieve this, \(\lambda \)  is also input to the mask prediction network as an auxiliary variable. As an implementation, we concatenate \(\lambda \)  to the encoder output in the feature dimension as shown in Fig. REF . After applying a mixture consistency projection layer [1]}, the loss value is calculated as the squared-error between the target SNRi, \(\lambda \) , and SNRi of the output signal as:
\(\mathcal {L}^{\mbox{\tiny {SNRi}}} &= \vert \lambda - \operatorname{SNRi}\vert ^2 + \beta \mathcal {L}^{\mbox{\tiny {SAR}}},\\\operatorname{SNRi}&= 10 \log _{10} \left( \frac{\Vert \mathbf {s} \Vert ^2}{\Vert \mathbf {y}_{:, 1} - \mathbf {s} \Vert ^2} \right) - 10 \log _{10} \left( \frac{\Vert \mathbf {s} \Vert ^2}{\Vert \mathbf {n} \Vert ^2} \right),\\\mathcal {L}^{\mbox{\tiny {SAR}}} &= -10 \log _{10}(\Vert \mathbf {s}\Vert ^2 / (\Vert \mathbf {e}_{\mbox{\tiny {artif}}}\Vert ^2 + \tau \Vert \mathbf {s}\Vert ^2)),\) 
